abacus
 An oriental counting device and calculator.
 Abelian group
 A group in which the binary operation is commutative, that is, ab=ba for all elements a abd b in the group.
 abscissa
 The xcoordinate of a point in a 2dimensional coordinate system.
 absolute value
 The positive value for a real number, disregarding the sign. Written x. For example, 3=3, 4=4, and 0=0.
 abundant number
 A positive integer that is smaller than the sum of its proper divisors.
 acceleration
 The rate of change of velocity with respect to time.
 acute angle
 An angle that is less than 90 degrees
 addition
 The process of adding two numbers to obraint heir sum.
 algebraic equation
 An equation of the form f(x)=0 where f is a polynomial.
 algebraic number
 A number that is the root of an algebraic polynomial. For example, sqrt(2) is an algebraic number because it is a solution of the equation x^{2}=2.
 alphametic
 A cryptarithm in which the letters, which represent distinct digits, form related words or meaningful phrases.
 altitude
 The altitude of a triangle is the line segment from one vertex that is perpendicular to the opposite side.
 amicable numbers
 Two numbers are said to be amicable if each is equal to the sum of the proper divisors of the other.
 angle
 The figure formed by two line segments or rays that extend from a given point.
 annulus
 The region enclosed by two concentric circles.
 arc
 A portion of a circle.
 area
 The amount of surface contained by a figure.
 arithmetic
 The type of mathematics that studies how to solve problems involving numbers (but no variables).
 arithmetic mean
 The arithmetic mean of n numbers is the sum of the numbers divided by n.
 automorphism
 An isomorphism from a set onto itslef.
 average
 Typically this refers to the arithmetic mean.
ball
 A sphere together with its interior.
 bar graph
 A type of chart used to compare data in which the length of a bar represents the size of the data.
 base
 In the expression x^{y}, x is called the base and y is the exponent.
 Bayes's Rule
 A rule for finding conditional probability.
 binary number
 A number written to base 2.
 binary operation
 A binary operation is an operation that involves two operands. For example, addition and subtraction are binary operations.
 bijection
 A onetoone onto function.
 binomial
 An expression that is the sum of two terms.
 binomial coefficient
 The coefficients of x in the expansion of (x+1)^{n}.
 biquadratic equation
 A polynomial equation of the 4th degree.
 bisect
 to cut in half.
 bit
 A binary digit.
 braces
 The symbols { and } used for grouping or to represent a set.
 byte
 The amount of memory needed to represent one character on a computer, typically 8 bits.
 Calculator
 A machine for performing arithemtical calculations.
 Caliban puzzle
 A logic puzzle in which one is asked to infer one or more facts from a set of given facts.
 cardinal number
 A number that indicates the quantity but not the order of things.
 catenary
 A curve whose equation is y = (a/2)(e^{x/a}+e^{x/a}). A chain suspended from two points forms this curve.
 ceiling function
 The ceiling function of x is the smallest integer greater than or equal to x.
 central angle
 An angle between two radii of a circle.
 centroid
 The center of mass of a figure. The centroid of a triangle is the intersection of the medians.
 cevian
 A line segment extending from a vertex of a triangle to the opposite side.
 Chebyshev polynomials

 chord
 The line joining two points on a curve is called a chord.
 circle
 The set of points equidistant from a given point (the center).
 circular cone
 A cone whose base is a circle.
 circumcenter
 The circumcenter of a triangle is the center of the circumscribed circle.
 circumcircle
 The circle circumscribed about a figure.
 circumference
 The boundary of a circle.
 cissoid
 A curve with equation y^{2}(ax)=x^{3}.
 coefficient
 The constant multipliers of the indeterminate variable in a polynomial. For example, in the polynomial x^{2}+3x+7, the coefficients are 1, 3, and 7.
 common denominator
 A multiple shared by the denominators of two or more fractions.
 complementary angles
 Two angles whose sum is 90^{o}.
 complex number
 The sum of a real number and an imaginary number, for example 3+4i where i=sqrt(1).
 compute
 To solve problems that use numbers.
 concave
 curved from the inside.
 cone
 A threedimensional solid that rises froma circular base to a single point at the top.
 congruent figures
 two geometric figures that are identical in size and shape.
 conic section
 The cross section of a right circular cone cut by a plane. An ellipse, parabola, and hyperbola are conic sections.
 coordinates
 Numbers that determine the position of a point.
 coprime
 Integers m and n are coprime if gcd(m,n)=1.
 cryptarithm
 A number puzzle in which an indicated arithmetical operation has some or all of its digits replaced by letters or symbols and where the restoration of the original digits is required. Each letter represents a unique digit.
 cube
 A solid figure bounded by 6 congruent squares.
 cubic equation
 A polynomial equation of degree 3.
 cyclic polygon
 A polygon whose vertices lie on a circle.
 cylinder
 A rounded threedimensional solid that has a flat circular face at each end.
data
 Facts that have been collected but not yet interpreted.
 decagon
 A polygon with 10 sides.
 decimal number
 A number written to the base 10.
 decimal point
 The period in a deimal number separating the integer part from the fractional part.
 deficient number
 A positive integer that is larger than the sum of its proper divisors.
 degree
 The degree of a term in one variable is the exponent of that variable. For example, the degree of 7x^{5} is 5.
 denominator
 In the fraction x/y, x is called the numerator and y is called the denominator.
 diagonal
 In a polygon, the line segment joining a vertex with another (nonadjacent) vertex is called a diagonal.
 diameter
 The longest chord of a figure. In a circle, a diameter is a chord that passes through the center of the circle.
 difference
 The difference between two numbers is what you get when you subtract one from the other.
 differential calculus
 That part of calculus that deals with the opeation of differentiation of functions.
 digimetic
 A cryptarithm in which digits represent other digits.
 digit
 In the decimal system, one of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
 dihedral angle
 The angle formed by two planes meeting in space.
 dimension
 The indication of how far something extends in space.
 disc
 A circle together with its interior.
 distributive law
 The formula a(x+y)=ax+ay.
 dividend
 In the expression "a divided by b", a is the divident and b is the divisor.
 division
 A basic arithmetical operation determining how many times one quantity is contained within another.
 divisor
 In the expression "a divided by b", a is the divident and b is the divisor.
 divisor
 The nonzero integer d is a divisor of the integer n if n/d is an integer.
 Diophantine equation
 An equation that is to be solved in integers.
 dodecagon
 A polygon with 12 sides.
 dodecahedron
 A solid figure with 12 faces A regular dodecahedron is a regular polyhedron with 12 faces. Each face is a rgular pentagon.
 domain
 The domain of a function f(x) is the set of x values for which the function is defined.
 domino
 Two congruent squares joined along an edge.
 duodecimal number system
 The system of numeration with base 12.
Egyptian fraction
 A number of the form 1/x where x is an integer is called an Egyptian fraction.
 eigenvalue
 characteristic value
 elementary function
 one of the functions: rational functions, trigonometric functions, exponential functions, and logarithmic functions.
 ellipse
 A plane figure whose equation isx^{2}/a^{2}+y^{2}/b^{2}=1.
 ellipsoid
 A solid figure whose equation is x^{2}/a^{2}+y^{2}/b^{2}+z^{2}/c^{2}=1.
 empty set
 The set with no elements in it.
 enumerable set
 A countable set.
 equation
 A statement that two expressions are equal to each other.
 equiangular polygon
 A polygon all of whose interior angles are equal.
 equichordal point
 A point inside a closed convex curve in the plane is called an equichordal point if all chords through that point have the same length.
 equilateral polygon
 A polygon all of whose sides are equal.
 equilateral triangle
 A triangle with three equal sides.
 escribed circle
 An escribed circle of a triangle is a circle tangent to one side of the triangle and to the extensions of the other sides.
 estimate
 A rough guess at the value of a number.
 Euler line
 The Euler line of a triangle is the line connecting the centroid and the circumcenter.
 Euler's constant
 The limit of the series 1/1+1/2+1/3+...+1/nln n as n goes to infinity. Its value is approximately 0.577216.
 even function
 A function f(x) is called an even function if f(x)=f(x) for all x.
 even number
 An integer that is divisible by 2.
 excenter
 The center of an excircle.
 excircle
 An escribed circle of a triangle.
 exponent
 In the expression x^{y}, x is called the base and y is called the exponent.
 exponential function
 The function f(x)=e^{x}.
 expoential function to base a
 The function f(x)=a^{x}.
 exradius
 An exradius of a triangle is the radius of an escribed circle.
face angle
 The plane angle formed by adjacent edges of a polygonal angle in space.
 factor (noun)
 An exact divisor of a number. This 7 is a factor of 28.
 factor (verb)
 To find the factors of a number.
 factorial
 n! (read n factorial) is equal to the product of the integers from 1 to n.
 Farey sequence
 The sequence obtained by arranging in numerical order all the proper fractions having denominators not greater than a given integer.
 Fermat number
 A number of the form 2^{2^n}+1.
 Fermat's spiral
 A parabolic spiral.
 Fibonacci number
 A member of the sequence 0, 1, 1, 2, 3, 5,... where each number is the sum of the previous two numbers.
 figurate numbers
 polygonal numbers
 finite group
 A group containing a finite number of elements.
 floor function
 The floor function of x is the greatest integer in x, i.e. the largest integer less than or equal to x.
 focal chord
 A chord of a conic that passes through a focus.
 focal radius
 A line segment from the focus of an ellipse to a point on the perimeter of the ellipse.
 foot of altitude
 The intersection of an altitude of a triangle with the base to which it is drawn.
 foot of line
 The point of intersection of a line with a line or plane.
 formula
 A concise statement expressing the symbolic relationship between two or more quantities.
 Fourier series
 A periodic function with period 2 pi.
 fraction
 An expression of the form a/b.
 frequency
 The number of times a value occurs in some time interval.
 frustum
 For a given solid figure, a related figure formed by two parallel planes meeting the given solid. In particular, for a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base. NOTE: this word is frequently incorrectly misspelled as frustrum.
Gaussian curve
 A normal curve.
 geoboard
 A flat board into which nails have been driven in a regular rectangular pattern. These nails represent the lattice points in the plane.
 geodesic
 The arc on a surface of shortest length joining two given points.
 geodesy
 A branch of mathematics dealing with the shape, size, and curvature of the Earth.
 geometric mean
 The geometric mean of n numbers is the nth root of the product of the numbers.
 geometric progression
 A sequence in which the ratio of each term to the preceding term is a given constant.
 geometric series
 A series in which the ratio of each term to the preceding term is a given constant.
 geometric solid
 The bounding surface of a 3dimensional portion of space.
 geometry
 The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties.
 Gergonne point
 In a triangle, the lines from the vertices to the points of contact of the opposite sides with the inscribed circle meet in a point called the Gergonne point.
 gnomon magic square
 A 3 X 3 array in which the elements in each 2 X 2 corner have the same sum.
 golden ratio
 (1+Sqrt[5])/2.
 golden rectangle
 A rectangle whose sides are in the golden ratio.
 graceful graph
 A graph is said to be graceful if you can number the n vertices with the integers from 1 to n and then label each edge with the difference between the numbers at the vertices, in such a way that each edge receives a different label.
 grad (or grade)
 1/100th of a right angle
 graph
 A graph is a set of points (called vertices) and a set of lines (called edges) joinging these vertices.
 great circle
 A circle on the surface of a sphere whose center is the center of the sphere.
 greatest common divisor
 The greatest common divisor of a sequence of integers, is the largest integer that divides each of them exactly.
 greatest common factor
 Same as greatest common divisor.
 greatest lower bound
 The greatest lower bound of a set of real numbers, is the largest real number that is smaller than each of the numbers in the set.
 group
 A mathematical system consisting of elements from a set G and a binary operation * such that
 x*y is a member of G whenever x and y are
 (x*y)*z=x*(y*z) for all x, y, and z
 there is an identity element e such that e*x=x*e=e for all x
 each member x in G has an inverse element y such that x*y=y*x=e
halfline
 A ray.
 halfplane
 The part of a plane that lies on one side of a given line.
 Hankel matrix
 A matrix in which all the elements are the same along any diagonal that slopes from northeast to southwest.
 harmonic analysis
 The study of the representation of functions by means of linear operations on characteristic sets of functions.
 harmonic division
 A line segment is divided harmonically by two points when it is divided externally and internally int he same ratio.
 harmonic mean
 The harmonic mean of two numbers a and b is 2ab/(a + b).
 hectare
 A unit of measurement in the metric system equal to 10,000 square meters (approximately 2.47 acres).
 helix
 The path followed by a point moving on the surface of a right circular cylinder that moves along the cylinder at a constant ratio as it moves around the cylinder. The parameteric equation for a helix is
 x=a cos t
y=a sin t
z=bt
 heptagon
 A polygon with 7 sides.
 hexagon
 A polygoin with 6 sides.
 hexagonal number
 A number of the form n(2n1).
 hexagonal prism
 A prism with a hexagonal base.
 hexahedron
 A polyhedron having 6 faces. The cube is a regular hexahedron.
 hexomino
 A sixsquare polyomino.
 Heronian triangle
 A triangle with integer sides and integer area.
 homeomorphism
 A onetoone continuous transformation that preserves open and closed sets.
 homomorphism
 A function that preserve the operators associated with the specified structure.
 horizontal line
 A line parallel to the earth's surface or the bottom of a page.
 hyperbola
 A curve with equation x^{2}/a^{2}y^{2}/b^{2}=1.
 hyperbolic spiral
 The curve whose equation in polar coordinates is r*theta=a.
 hyperboloid
 A geometric solid whose equation is x^{2}/a^{2}+y^{2}/b^{2}z^{2}/c^{2}=1 orx^{2}/a^{2}+y^{2}/b^{2}z^{2}/c^{2}=1.
 hypotenuse
 The longest side of a right triangle.
icosahedron
 A polyhedron with 20 faces.
 idempotent
 The element x in some algebraic structure is called idempotent if x*x=x.
 imaginary axis
 The yaxis of an Argand diagram.
 imaginary number
 A complex number of the form xi where x is real and i=sqrt(1).
 imaginary part
 The imaginary part of a complex number x+iy where x and y are real is y.
 incenter
 The incenter of a triangle is the center of its inscribed circle.
 incircle
 The circle inscribed in a given figure.
 inequality
 The statement that one quantity is less than (or greater than) another.
 infinite
 becoming large beyond bound.
 infinitesimal
 A variable that approaches 0 as a limit.
 infinity
 A reference to a quantity larger than any specific integer.
 inflection
 A point of inflection of a plane curve is a point where the curve has a stationary tangent, at which the tangent is changing from rotating in one direction to rotating in the oppostie direction.
 injection
 A onetoone mapping.
 inscribed angle
 The angle formed by two chords of a curve that meet at the same point on the curve.
 integer
 One of the numbers ..., 3, 2, 1, 0, 1, 2, 3, ...
 intersect
 Two figures are said to intersect if they meet or cross each other.
 irrational number
 A number that is not rational.
 isogonal conjugate
 Isogonal lines of a triangle are cevians that are symmetric with respect to the angle bisector. Two points are isogonal conjugates if the corresponding lines to the vertices are isogonal.
 isometry
 A length preserving map.
 isosceles tetrahedron
 A tetrahedron in which each pair of opposite sides have the same length.
 isosceles triangle
 A triangle with two equal sides.
 isosceles trapezoid
 Ain which the two nonparallel sides have the same length.
 isotomic conjugate
 Two points on the side of a triangle are isotomic if they are equidistant from the midpoint of that side. Two points inside a triangle are isotomic conjugates if the corresponding cevians through these points meet the opposite sides in isotomic points.
joint probability function
 A function that gives the probability that each of two or more random variables takes at a particular value.
 joint variation
 A variation in which the values of one variable depend upon those of 2 or more variables.
 Jordan curve
 A simple closed curve.
 Jordan matrix
 A matrix whose diagonal elements are all equal (and nonzero) and whose elements above the principal diagonal are equal to 1, but all other elements are 0.
 joule
 A unit of energy or work.
 jump discontinuity
 A discontinuity in a function where the left and righhand limits exist but are not equal to each other.
kilometer
 A unit of length equal to 1,000 meters.
 kinematics
 A branch of mechanics dealing with the motion of rigid bodies without reference to their masses or the forces acting on the bodies.
 kite
 A quadrilateral which has two pairs of adjacent sides equal.
 knight's tour
 A knight's tour of a chessboard is a sequence of moves by a knight such that each square of the board is visited exactly once.
 knot
 A curve in space formed by interlacing a piece of string and then joining the ends together.
 knot
 a unit of speed in navigation equal to one nautical mile per hour.
Ltetromino
 A tetromino in the shape of the letter L.
 latera recta
 plural of lattice rectum.
 latin square
 An n X n array of numbers in which only n numbers appear. No number appears more than once in any row or column.
 latitude
 The angular distance of a point on the Earth from the equator, measured along the meridian through that point.
 lattice point
 A point with integer coordinates.
 latus rectum
 A chord of an ellipse passing through a focus and perpendicular to the major axis of the ellipse.Plural: latera recta.
 least common multiple
 The least common multiple of a set of integers is the smallest integer that is an exact multiple of every number in the set.
 least upper bound
 The least upper bound of a set of numbers is the smallest number that is larger than every member of the set.
 lemata
 plural of lemma.
 lemma
 A proposition that is useful mainly for the proof of some other theorem.
 length
 The straight line distance between two points.
 Legendre polynomials

 line
 A geometrical figure that has length but no width.
 linear function
 A function of the form y=ax+b.
 line graph
 A chart that shows data by means of points connected by lines.
 line segment
 The part of a line between two given distinct points on that line (including the two points).
 locus
 The set of all points meeting some specified condition.
 logic
 The study of the formal laws of reasoning.
 lowest common denominator
 The smallest number that is exactly divisible by each denominator of a set of fractions.
 loxodrome
 On a sphere, a curve that cuts all parallels under the same angle.
 lowest common denominator
 The smallest multiple shared by the denominators of a set of fractions.
 lowest terms
 A fraction is said to be in lowest terms if its numerator and denominator have no common factor.
 Lucas number
 A member of the sequence 2, 1, 3, 4, 7,... where each number is the sum of the previous two numbers. L_{0}=2, L_{1}=1, L_{n}=L_{n1}+L_{n2}.
 lune
 The portion of a sphere between two great semicircles having common endpoints (including the semicircles).
magic square
 A square array of n numbers such that sum of the n numbers in any row, column, or main diagonal is a constant (known as the magic sum).
 magic tour
 If a chess piece visits each square of a chessboard in succession, this is called a tour of the chessboard. If the successive squares of a tour on an n X n chessboard are numbered from 1 to n^2, in order, the tour is called a magic tour if the resulting square is a magic square.
 main diagonal
 In the matrix [a_{ij}], the elements a_{11}, a_{22}, ..., a_{nn}.
 major axis
 The major axis of an ellipse is it's longest chord.
 Malfatti circles
 Three equal circles that are mutually tangent and each tangent to two sides of a given triangle.
 maximum
 The largest of a set of values.
 matrix
 A rectangular array of elements.
 mean
 Same as average.
 medial triangle
 The triangle whose vertices are the midpoints of the sides of a given triangle.
 median
 The median of a triangle is the line from a vertex to the midpoint of the opposite side.
 median
 When a set of numbers is ordered from smallest to largest, the median number is the one in the middle of the list.
 Mersenne number
 A number of the form 2^{p}1 where p is a prime.
 Mersenne prime
 A Mersenne number that is prime.
 midpoint
 The point M is the medpoint of line segment AB if AM=MB. That is, M is halfway between A and B.
 minor axis
 The minor axis of an ellipse is its smallest chord.
 minimum
 The smallest of a set of values.
 mode
 The most frequently occurring value in a sequence of numbers.
 modulo
 The integers a and b are said to be congruent modulo m if ab is divisible by m.
 monomial
 An algebraic expression consisting of just one term.
 monotone
 A sequence is monotone if its terms are increasing or decreasing.
 monic polynomial
 A polynomial in which the coefficient of the term of highest degree is 1.
 monochromatic triangle
 A triangle whose vertices are all colored the same.
 multinomial
 An algebraic expression consisting of 2 or more terms.
 multiple
 The integer b is a multiple of the integer a if there is an integer d such that b=da.
 multiplication
 The basic arithemtical operation of repeated addition.
nadir
 The point on the celestial spehere in the direction downwards of the plumbline.
 Nagel point
 In a triangle, the lines from the vertices to the points of contact of the opposite sides with the excircles to those sides meet in a point called the Nagel point.
 natural number
 Any one of the numbers 1, 2, 3, 4, 5, ... .
 negative number
 A number smaller than 0.
 nine point center
 In a triangle, the circumcenter of the medial triangle is called the nine point center.
 nine point circle
 In a triangle, the circle that passes through the midpoints of the sides is called the nine point circle.
 nomograph
 A graphical device used for computation which uses a straight edge and several scales of numbers.
 nonagonal number
 A number of the form n(7n5)/2.
 nonary
 associated with 9
 normal
 perpendicular
 null hypothesis
 The null hypothesis is the hypothesis that is being tested in a hypothesistesting situation.
 null set
 the empty set
 number line
 A line on which each point represents a real number.
 number theory
 The study of integers.
 numeral
 A symbol that stands for a number.
 numerator
 In the fraction x/y, x is called the numerator and y is called the denominator.
 numerical analysis
 The study of methods for approximation of solutions of various classes of mathematical problems including error analysis.
oblate spheroid
 An ellipsoid produced by rotating an ellipse through 360^{o} about its minor axis.
 oblique angle
 an angle that is not 90^{o}
 oblique coordinates
 A coordinate system in which the axes are not perpendicular.
 oblique triangle
 A triangle that is not a right triangle.
 obtuse angle
 an angle larger than 90^{o} but smaller than 180^{o}
 obtuse triangle
 A triangle that contains an obtuse angle.
 octagon
 A polygon with 8 sides.
 octahedron
 A polyhedron with 8 faces.
 octant
 any one of the 8 portions of space dtermined by the 3 coordinate planes.
 odd function
 A function f(x) is called an odd function if f(x)=f(x) for all x.
 odd number
 An integer that is not divisible by 2.
 one to one
 A function f is said to be one to one if f(x)=f(y) implies that x=y.
 onto
 A function f is said to map A onto B if for every b in B, there is some a in A such f(a)=b.
 open interval
 An interval that does not include its two endpoints.
 ordered pair
 A pair of numbers in which one number is distinguished as the first number and the other as the second number of the pair
 ordinal number
 A number indicating the order of a thing in a series
 ordinate
 The ycoordinate of a point in the plane.
 origin
 The point in a coordinate plane with coordinates (0,0).
 orthic triangle
 The triangle whose vertices are the feet of the altitudes of a given triangle.
 orthocenter
 The point of intersection of the altitudes of a triangle.
palindrome
 A positive integer whose digits read the same forward and backwards.
 palindromic
 A positive integer is said to be palindromic with respect to a base b if its representation in base b reads the same from left to right as from right to left.
 pandiagonal magic square
 A magic square in which all the broken diagonals as well as the main diagonals add up to the magic constant.
 pandigital
 A decimal integer is called pandigital if it contains each of the digits from 0 to 9.
 paraboloid
 A paraboloid of revolution is a surface of revolution produced by rotating a parabola about its axis.
 parallel
 Two lines in the plane are said to be parallel if they do not meet.
 parallelogram
 A quadrilateral whose opposite sides are parallel.
 parallelepiped
 A prism whose bases are parallelograms.
 parentheses
 The symbols ( and ) used for grouping expressions.
 Pascal's triangle
 A triangular array of binomial coefficients.
 pedal triangle
 The pedal triangle of a point P with respect to a triangle ABC is the triangle whose vertices are the feet of the perpendiculars dropped from P to the sides of triangle ABC.
 Pell number
 The nth term in the sequence 0, 1, 2, 5, 12,... defined by the recurrence
P_{0}=0, P_{1}=1, and P_{n}=2P_{n1}+P_{n2}.
 pentagon
 A polygon with 5 sides.
 pentagonal number
 A number of the form n(3n1)/2.
 pentomino
 A fivesquare polyomino.
 percent
 A way of expressing a number as a fraction of 100.
 perfect cube
 An integer is a perfect cube if it is of the form m^{3} where m is an integer.
 perfect number
 A positive integer that is equal to the sum of its proper divisors. For example, 28 is perfect because 28=1+2+4+7+14.
 perfect power
 An integer is a perfect power if it is of the form m^{n} where m and n are integers and n>1.
 perfect square
 An integer is a perfect square if it is of the form m^{2} where m is an integer.
 perimeter
 The distance around the edge of a multisided figure.
 perpendicular
 Two straight lines are said to be perpendicular if they meet at right angles.
 pi
 The ratio of the circumference of a circle to its diameter.
 pie chart
 A type of chart in which a circle is divided up into portions in which the area of each portion represents the size of the data.
 place value
 Within a number, each digit is given a place value depending on it's location within the number.
 plane
 A twodimensional area in geometry.
 point
 In geometry, a point represents a position, but has no size.
 polygon
 A plane figure with many sides.
 polyomino
 A planar figure consisting of congruent squares joined edgetoedge.
 positive number
 A number larger than 0.
 power
 A number multiplied by itself a specified number of times.
 practical number
 A practical number is a positive integer m such that every natural number n not exceeding m is a sum of distinct divisors of m.
 prime
 A prime number is an integer larger than 1 whose only positive divisors are 1 and itself.
 primitive Pythagorean triangle
 A right triangle whose sides are relatively prime integers.
 primitive root of unity
 The complex number z is a primitive nth root of unity if z^{n}=1 but z^{k} is not equal to 1 for any positive integer k less than n.
 probability
 The chance that a particular event will happen.
 product
 The result of multiplying two numbers.
 pronic number
 A number of the form n(n+1).
 proper divisor
 The integer d is a proper divisor of the integer n if 0<d<n and d is a divisor of n.
 proportion
 A comparison of ratios.
 pyramid
 A threedimensional solid whose base is a polygon and whose sides are triangles that come to a point at the top.
 Pythagorean triangle
 A right triangle whose sides are integers.
 Pythagorean triple
 An ordered set of three positive integers (a,b,c) such that a^{2}+b^{2}=c^{2}.
QED
 Abbreviation for quod erat demonstrandum, used to denote the end of a proof.
 quadrangle
 A closed broken line in the plane consisting of 4 line segments.
 quadrangular prism
 A prism whose base is a quadrilateral.
 quadrangular pyramid
 A pyramid whose base is a quadrilateral.
 quadrant
 Any one of the four portions of the plane into which the plane is divided by the coordinate axes.
 quadratfrie
 square free
 quadratic equation
 An equation of the form f(x)=0 where f(x) is a second degree polynomial. That is, ax^{2}+bx+c=0.
 quadrature
 The quadrature of a geometric figure is the determination of its area.
 quadric curve
 The graph of a second degree equation in two variables.
 quadric surface
 The graph of a second degree equation in three variables.
 quadrilateral
 A geometric figure with four sides.
 quadrinomial
 An algebraic expression consisting of 4 terms.
 quartic polynomial
 A polynomial of degree 4.
 quartile
 The first quartile of a sequence of numbers is the number such that one quuarter of the numbers in the sequence are less than this number.
 quintic polynomial
 A polynomial of degree 5.
 quotient
 The result of a division.
radian
 A unit of angular measurement such that there are 2 pi radians in a complete circle. One radian = 180/pi degrees. One radian is approximately 57.3^{o}.
 radical axis
 the locus of points of equal power with respect to two circle.
 radical center
 The radical center of three circles is the common point of interesection of the radical axes of each pair of circles.
 radii
 Plural of radius.
 radius
 The length of a stright line drown from the center of a circle to a point on its circumference.
 radix point
 The generalization of decimal point to bases of numeration other than base 10.
 range
 The set of values taken on by a function.
 rate
 A way of comparing two quantities.
 ratio
 quotient of two numbers.
 rational number
 A rational number is a number that is the ratio of two integers. All other real numbers are said to be irrational.
 real axis
 The xaxis of an Argand diagram.
 real part
 The real number x is called ther eal part of the complex number x+iy where x and y are real and i=sqrt(1).
 real variable
 A variable whose value ranges over the real numbers.
 reciprocal
 The reciprocal of the number x is the number 1/x.
 rectangle
 A quadrilateral with 4 right angles.
 reflex angle
 An angle between 180^{o} and 360^{o}.
 remainder
 The number left over when one number is divided by another.
 repdigit
 An integer all of whose digits are the same.
 repeating decimal
 A decimal whose digits eventually repeat.
 repunit
 An integer consisting only of 1's.
 rhombus
 A parallelogram with four equal sides.
 right angle
 an angle formed by two perpendicular lines; a 90^{o} angle.
 right triangle
 A triangle that contains a right angle.
 roman numerals
 A system of numeration used by the ancient Romans.
 root of unity
 A solution of the equation x^{n}=1, where n is a positive integer.
 roundoff error
 The error accumulated during a calculation due to rounding intermediate results.
 rounding
 The process of approximating a number to a nearby one.
 ruled surface
 A surface formed by moving a straight line (called the generator).
 rusty compass
 A pair of compasses that are fixed open in a given position.
scalene triangle
 A triangle with unequal sides.
 secant
 A straight lien that meets a curve in two or more points.
 semimagic square
 A square array of n numbers such that sum of the n numbers in any row or column is a constant (known as the magic sum).
 sequence
 A collection of numbers in a prescribed order: a_{1}, a_{2}, a_{3}, a_{4}, ...
 series
 The sum of a finite or infinite sequence
 set
 A collection of objects.
 similar figures
 Two geometric figures are similar if their sides are in proportion and all their angles are the same.
 skeleton division
 A long division in which most or all of the digits have been replaced by asterisks to form a cryptarithm.
 slide rule
 A calculating device consisting of two sliding logarithmic scales.
 solid
 A threedimensional figure.
 solid of revolution
 A solid formed by rotation a plane figure about an axis in threespace.
 solidus
 The slanted line in a fraction such as a/b dividing the numerator from the denominator.
 sphere
 The locus of pointsin threespace that are a fixed distance froma given point (called the center).
 spherical trigonometry
 The branch of mathematics dealing with measurements on the sphere.
 square
 A quadrilateral with 4 equal sides and 4 right angles.
 square free
 An integer is said to be square free if it is not divisible by a perfect square, n^{2}, for n>1.
 square number
 A number of the form n^{2}.
 square root
 The number x is said to be a square root of y if x^{2} = y.
 Stirling numbers

 subtraction
 A basic operation of arithemtic in which you take away one number from another.
 sum
 The result of adding two or more numbers.
 supplementary
 Two angels are supplementary of they add up to 180^{o}.
 surface area
 The measure of a surface of a threedimensional solid indicating how large it is.
 symmedian
 Reflection of a median of a triangle about the corresponding angle bisector.
tangent
 A line that meets a smooth curve at a single point and does not cut across the curve.
 tautology
 A sentence that is true because of its logical structure.
 tetrahedron
 A polyhedron with four faces.
 tetromino
 A foursquare polyomino.
 Toeplitz matrix
 A matrix in which all the elements are the same along any diagonal that slopes from northwest to southeast.
 torus
 A geometric solid in the shape of a donut.
 trace
 The trace of a matrix is the sum of the terms along the principal diagonal.
 transcendental number
 A number that is not algebraic.
 trapezium
 A quadrilateral in which no sides are parallel.
 trapezoid
 A quadrilateral in which two sides are parallel.
 tree
 A tree is a graph with the property that there is a unique path from any vertex to any other vertex traveling along the edges.
 triangle
 A geometric figure with three sides.
 triangular number
 A number of the form n(n+1)/2.
 trinomial
 An algebraic expression consisting of 3 terms.
 tromino
 A threesquare polyomino.
 truncated pyramid
 A section of a pyramid between its base and a plane parallel to the base.
 twin primes
 Two prime numbers that differ by 2. For example, 11 and 13 are twin primes.
unilateral surface
 A surface with only one side, such as a Moebius strip.
 unimodal
 A finite sequence is unimodal if it first increases and then decreases.
 unimodular
 A square matrix is unimodular if its determinant is 1.
 unit circle
 A unit circle is a circle with radius 1.
 unit cube
 A cube with edge length 1.
 unit fraction
 A fraction whose numerator is 1.
 unit square
 A unit square is a square of side length 1.
 unitary divisor
 A divisor d of c is called unitary if gcd(d,c/d) = 1.
 unity
 one
variable
 A symbol whose value can change.
 velocity
 The rate of change of position.
 vertical line
 A line that runs up and down and is perpendicular to a horizontal line.
 vigesimal
 related to intervals of 20.
 vinculum
 The horizontal bar in a fraction separating the numerator from the denominator.
 volume
 The measure of spce occupied by a solid body.
 vulgar fraction
 A common fraction.
weak inequality
 An inequality that permits the equality case. For example, a is less than or equal to b.
 wff
 A wellformed formula.
 whole number
 A natural number.
 winding number
 The number of times a closed curve in the plane passes around a given point in the counterclockwise direction.
 witch of Agnesi
 A curve whose equation is x^{2}y=4a^{2}(2ay).
X
 Roman numeral for 10.
 xaxis
 The horizontal axis in the plane.
 xintercept
 The point at which a line crosses the xaxis.
 Xpentomino
 A pentomino in the shape of the letter X.
yaxis
 The vertical axis in the plane.
 yintercept
 The point at which a line crosses the yaxis.
 yard
 A measure of length equal to 3 feet.
 year
 A measure of time equal to the period of one revolution of the earth about the sun. Approximately equal to 365 days.
zintercept
 The point at which a line crosses the zaxis.
 zero
 0
 zero divisors
 Nonzero elements of a ring whose product is 0.
 zero element
 The element 0 is a zero element of a group if a+0=a and 0+a=a for all elements a.
 zeta function

 zone
 The portion of a sphere between two parallel planes.

